Question

Verify commutativty of addition of rational numbers for each of the following pairs of rotional numbers:

\[\frac{- 11}{5} \text{and} \frac{4}{7}\]

Answer 1

\[\text{Commutativity of the addition of rational numbers means that if} \frac{a}{b} \text{and} \frac{c}{d} \text{are two rational numbers, then} \frac{a}{b} + \frac{c}{d} = \frac{c}{d} + \frac{a}{b} . \]
\[\text{We have}\frac{- 11}{5} \text{and} \frac{4}{7} . \]
\[ \therefore \frac{- 11}{5} + \frac{4}{7} = \frac{- 11 \times 7}{5 \times 7} + \frac{4 \times 5}{7 \times 5} = \frac{- 77}{35} + \frac{20}{35} = \frac{- 77 + 20}{35} = \frac{- 57}{35}\]
\[ \frac{4}{7} + \frac{- 11}{5} = \frac{4 \times 5}{7 \times 5} + \frac{- 11 \times 7}{5 \times 7} = \frac{20}{35} + \frac{- 77}{35} = \frac{20 - 77}{35} = \frac{- 57}{35}\]
\[ \therefore \frac{- 11}{5} + \frac{4}{7} = \frac{4}{7} + \frac{- 11}{5}\]
\[ \text{Hence verified .} \]